I'm also having huge problems uploading to YouTube and get the same error message as you, Connection with the remote server failed. I also seen another error message simply saying Upload failed and the last time I got both these messages. The conversion always completes successfully but it's when Action! is about to start uploading the video to YouTube these error messages appear.
I have been able to upload once and that time I checked the option to have Action! automatically split the video into several parts and I chose 15 mins. Not sure if this has anything to do with this problem because looking at the error message that Action! fails to connect to the remote server doesn't look like it would be any different looking at the size of the movie you want to upload.
I also created my own thread regarding this problem but so far no replies and now I've also sent a support request to
support@mirillis.com
I really do hope there's a way to fix this because just like you being able to upload directly to YouTube from within the software was one of the reasons I decided to buy it.